Small underground nuclear explosions need to be confidently detected and identified in regions of the world where they have never occurred. We are developing a parametric model of the nuclear explosion seismic source spectrum derived from regional phases (Pn, Pg, Sn, and Lg) that is compatible with earthquake-based geometrical spreading and attenuation. Earthquake spectra are fit with a generalized version of the Brune spectrum, which is a three-parameter model that describes the long-period level, corner-frequency, and spectral slope at high frequencies. These parameters are then correlated with near-source geology and containment conditions. There is a correlation of high gas-porosity (low strength) with increased spectral slope. However, there are trade-offs between the slope and corner-frequency, which we try to independently constrain using Mueller-Murphy relations and coda-ratio techniques. The relationship between the parametric equations and the geologic and containment conditions will assist in our physical understanding of the nuclear explosion source. The achievable goal of our parametric model development is to be able to predict observed local and regional distance seismic amplitudes for event identification and yield determination in regions with incomplete or no prior history of underground nuclear testing.